With almost 1,000 branches in prime high street sites up and down the country, the Co-operative Bank is poised to become a major competitor to the big four high street banks.

Or so hope the UK's largest mutual and the coalition government – which is keen to promote competition in retail banking – after Lloyds Banking Group last week edged closer to agreeing terms on a long-awaited transaction to sell 632 of its branches to the Co-op.

Lloyds has been forced to sell the branches under EU state aid rules, because of the £20bn of taxpayer funds it received during the banking crisis.

The deal is least three months behind the timetable set by Lloyds when it parcelled up the branches for sale under the codename "Project Verde", and a crucial "heads of agreement" needed to push the final buttons will still not be secured for a few more weeks. But at last a deal is in sight that could transform the group that started as a grocery wholesaler in Rochdale into a formidable force in banking.

The sale would see the number of Co-op branches bank triple and the enlarged group account for 7% of the all-important current account market. The big four – Lloyds, RBS, Barclays and HSBC – have a 75% market share in that area that has proved impossible to crack for decades.

The Co-op's audacious expansion plans, laid over many months, could now look exquisitely well-timed. The scandal over interest rate fixing, the NatWest computer crisis – which left millions of customers unable to use their accounts – and the mis-selling of interest rate swap products to small businesses have left a growing number of customers wondering whether they can trust conventional banks.

The Move Your Money campaign, a grassroots organisation urging customers to desert the mainstream lenders and bank with mutuals, has seen a fivefold increase in hits on its website over the past fortnight.

He argues that mutually owned institutions tend to pay lower bonuses and behave more cautiously: "They're not trying to generate maximum shareholder returns, so their bonuses tend to be tied to customer satisfaction."

Even so, Ian Gordon, banking analyst at Investec, thinks the Co-op may "still not be of a big enough scale to compete with the big four". Others say bolting on the Lloyds branches – which bring a 4.5% share of the current account market – to an existing, albeit tiny, player should help. The independent commission on banking, chaired by Sir John Vickers, had been concerned that on their own the Verde branches would be "on the borderline of sub-scale banks that failed to grow significantly in the past".

Ed Mayo, secretary-general of Co-operatives UK, the umbrella organisation for mutuals from local bakeries to the John Lewis Partnership, says: "We've had a drip, drip, drip of scandals, characterised by a herd mentality. That's why there's such an interest in a co-operative, mutual model."

He adds that mutuals are less likely to follow the herd, or the short-term return: "They behave in different ways, not because they've got 'co-operative' over the door, but because they work to different incentives. If you're owned by your customers, you're not going to fleece them in the same way."

He pointed out that the UK, where a swath of building societies demutualised in the late 1980s, has an unusually small co-operative banking sector. In the Netherlands, for example, half the population banks with a mutual.

Many politicians, too, would welcome a successful alternative to the standard high street financial institutions: but it remains to be seen whether the Co-op can retain its distinctive culture and make a success of its radical expansion.